Finite Group Databasebeta

C2×D608 #14565933

order2432
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×D608

Splittings

FittingC2×C19×C32 ⋊ C2
SylowC19 ⋊ C2×D32

Subgroups

subgroupG/H
centerC22D304
commutator, cosocleC16×C19C23
FrattiniC16C22×D19
FittingC2×C19×C32C2
socleC22×C19D16
hypercenterC2×C32D19
hypocenterC19C2×D32
LCSG ▷ C16×C19 ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

614 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#18070416, #18070418, #18070428, …
maximal normal subgroup of#18070416, #18070418, #18070428, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6808);